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Grade 10 Advanced About 15 min Version 1 Awaiting review Premium

Apparent depth: why pools look shallow

Light from a coin at the bottom of a tank bends away from the normal as it leaves the water. Your eye assumes light travels in straight lines, so it traces the rays back to a point above the real coin. The coin seems nearer the surface than it is: its apparent depth is less than its real depth. Looking straight down, refractive index n = real depth ÷ apparent depth. That is why pools and rivers are deeper than they look.

What you will learn

  • Explain apparent depth using refraction.
  • Calculate refractive index from real and apparent depth.
  • Explain why water is often deeper than it looks.

Before you start

  • Know that light bends away from the normal leaving a denser medium.

Materials

  • A coin, water and clear cooking oil

Equipment

  • Tall clear tank or measuring cylinder
  • Travelling microscope or a pin and ruler to locate the image

Procedure

  1. Put the coin under 10 cm, 20 cm and 40 cm of water, recording the apparent depth each time.
  2. Fill the tank with oil and record the apparent depth at one depth.
  3. Calculate real depth ÷ apparent depth for each.

How this simulation is simplified

  • You look straight down, so the simple ratio n = real ÷ apparent depth applies.
  • Refractive indices: water 1.33, clear cooking oil 1.47.